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Murray shouted "wake up!" during one of many frustrating moments on Rod Laver Arena but a dozy display proved sufficient as the Scot sealed a 7-5 7-6 (7/5) 6-2 victory.
He will now face Russian teenager Andrey Rublev, the world number 152 who had earlier registered a surprise win over Yen-Hsun Lu.
Murray, walking out on court at just after 3pm local time, was not addressed as 'Sir' in the announcer's introduction but that will have been of little concern to the top seed, who insisted in his post-match interview that "Andy is definitely fine". Instead, the Briton is likely keen to continue where he left off last season as he chases his first title in Melbourne, where he has reached the final five times but never been crowned champion.
Chelsea goalkeeper Thibaut Courtois believes his team sent a message to their rivals with their win over Leicester City without Diego Costa.
Costa is apparently unsettled by an offer from the Chinese Super League, while head coach Antonio Conte said the Spain international was battling a back injury.
Most important goal of the weekend… Zlatan Ibrahimovic
There are not many people who have the self-belief of Zlatan Ibrahimovic. As much as he does disappear occasionally, and fail to take as many of his chances as a man of his self-declared talent should do, he is never cowed. His arrogance is self-fulfilling. If he didn’t think he was the best, he would end up embarrassed by his occasional failures, and be worse for it. He is sustained by self-confidence as much as anything else.
Chelsea or China? This is the simple, if slightly unusual, choice that seems to face many Brazilian footballers at some point in their Stamford Bridge careers.
For the likes of Ramires and Oscar it was a straight-forward case of take the money and run, but Diego Costa (yes he is Brazilian really, even if he pretends to be Spanish) has to make things typically dramatic. As such, Monday’s papers are filled with various theories about the striker’s decision between hard-earned Premier League glory and decadent Oriental oblivion.
Do not expect any Tottenham players to be lured to the Chinese Super League as Harry Kane and Co. challenge for silverware.
Oscar made a record-breaking move to Shanghai SIPG from Premier League leaders Chelsea, while former team-mate Diego Costa has been tipped to join the likes of Carlos Tevez, Hulk, Axel Witsel, Ezequiel Lavezzi and Ramires in China.